Multiple-scales analysis of cosmological perturbations in brane-worlds

TL;DR

This paper introduces a new approximation method for analyzing cosmological tensor perturbations in brane-world models, effectively avoiding coordinate singularities and revealing mode-mixing effects at higher orders.

Contribution

A novel approximation technique for solving tensor perturbation equations in brane-world cosmology that circumvents coordinate singularities and clarifies mode interactions.

Findings

Zero-mode reproduces standard 4D perturbation evolution

Next order reveals mode-mixing effects

Zero-mode does not source other modes at higher order

Abstract

We present a new approximation method for solving the equations of motion for cosmological tensor perturbations in a Randall-Sundrum brane-world model of the type with one brane in a five-dimensional anti-de Sitter spacetime. This method avoids the problem of coordinate singularities inherent in some methods. At leading order, the zero-mode solution replicates the evolution of perturbations in a four-dimensional Friedmann-Robertson-Walker universe in the absence of any tensor component to the matter perturbation on the brane. At next order, there is a mode-mixing effect, although, importantly, the zero-mode does not source any other modes.